4. Two lines intersect to form $$ \angle A B C $$. One step in constructing a line parallel to $$ B C $$ through point $$ A $$ is to construct an angle congruent to $$ \angle A B C $$ with vertex $$ A $$. Which theorem can you use to prove that the line you constructed is parallel to the given line? (A) Same-Side Interior Angles Theorem (B) Converse of the Same-Side (C) Corresponding Angles Theorem (D) Converse of the Corresponding (D) Angles Theorem

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(C) Corresponding Angles Theorem To determine which theorem can be used to prove that the line constructed through point $$ A $$ is parallel to line $$ BC $$, we need to consider the relationship between the angles formed. When you construct an angle congruent to $$ \angle ABC $$ at point $$ A $$, you are effectively creating an angle that corresponds to $$ \angle ABC $$ when considering the transversal formed by the line through $$ A $$ and line $$ BC $$. The theorem that states that if two lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel is known as the **Corresponding Angles Theorem**. Thus, the correct answer is: (C) Corresponding Angles Theorem

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